SOLUTION: Please help!! Am having great difficulty! The problem: Use the fact that if A= a b c d , then A^-1 = 1/ad-bc * d -b

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Question 392758: Please help!! Am having great difficulty! The problem:
Use the fact that if A= a b
c d , then A^-1 = 1/ad-bc * d -b
-c a
to find the inverse of each matrix, if possible. Check that AA^-1=I2 and
A^-1A=I2.
A= 6 -3
-2 1
Thank you sooo much to whomever responds!

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Finding the Inverse of a 2x2 Matrix

To find the inverse of the matrix A=%28matrix%282%2C2%2C6%2C-3%2C-2%2C1%29%29, we can follow these steps:

Step 1) Find the determinant



The determinant of %28matrix%282%2C2%2C6%2C-3%2C-2%2C1%29%29 is abs%28matrix%282%2C2%2C6%2C-3%2C-2%2C1%29%29=0. So this means that d=0

Since the determinant is equal to zero, this means that no inverse exists.

Remember, the inverse of %28matrix%282%2C2%2Ca%2Cb%2Cc%2Cd%29%29 is %281%2Fd%29%28matrix%282%2C2%2Cd%2C-b%2C-c%2Ca%29%29.

If d=0, then a division by zero occurs, which is NOT allowed.

So we can stop here.


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Answer:

So the inverse of A=%28matrix%282%2C2%2C6%2C-3%2C-2%2C1%29%29 does NOT exist since d=0 (ie the determinant is 0).




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Jim